Animated Double Pendulum
Editor's Note: This file was selected as MATLAB Central Pick of the Week
For animation, the program uses Matlab's normal plot command combined with the drawnow command. It is based on the ode45 solution of the corresponding differential equations.
Comprehensive documentation is provided, including a sketch of the most important steps of how to derive the equations of motion. A simple Mathematica notebook contains all of the manipulations.
Start the program via >> double_pendulum_init
You can adapt parameters such as rod lengths, masses and initial angular positions and velocities in the double_pendulum_init.m file.
It might be interesting to implement some features in future versions, such as angular time dependence plots, phase space portraits or Poincaré sections.
Have fun observing the rich dynamic behaviour of this simple, but mostly chaotic system :-)
Cite As
Alexander Erlich (2021). Animated Double Pendulum (https://www.mathworks.com/matlabcentral/fileexchange/27212-animated-double-pendulum), MATLAB Central File Exchange. Retrieved .
Comments and Ratings (16)
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- Mathematics > Numerical Integration and Differential Equations >
- Graphics > 2-D and 3-D Plots > Animation >
- Science, Engineering and Industry > Sciences > Physics > Nonlinear Dynamics >
- Physical and Event-Based Modeling > Physical Modeling > Simscape Multibody > Multibody Modeling > Assembly > Pendulums >
- Science, Engineering and Industry > Sciences > Physics > General Physics > Classical Mechanics >
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Acknowledgements
Inspired: SimplePendulum
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Does not run.
To Liu. Yes, you are right, the built-in Matlab ODE solvers do not conserved the energy in Hamiltonian systems. You need to use a different solver, for example based on the Verlet method
Does anyone know why this simulation fails at a larger time than 100 seconds(1000 seconds for example)? It seems that the total energy is not conserved. could it be a Matlab problem given the Lagrange forms are correct?
Very nice illustration. I am curious however to why the pendulum starts to move when initializing it at it's upward equilibrium
(phi1 = pi;dtphi1 = 0;phi2 = pi;dtphi2 = 0;)
Is this due to approximation mistakes by matlab where the number pi is represented with a finite number of decimals?
amazing, this program could be a base reference for further works.
Results are very inconsistent with other projects and online simulators, but they seem to use iterative calculations and not ivp deq's. Also equations in m-file are inconsistent with pdf documentation. Can you please elaborate on that?
wonderful!
10!